April 13, 2023

Circles

1. Circumference, diameter and radius.

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April 13, 2023

Here is a circle.

The distance all the way round the perimeter is known as the circumference.Any straight line that touches the circle at a single point is known as a tangent.The diameter is a straight line through the centre, from one side to the other.The radius is a line from the centre, to the circumference.Any straight line that crosses the circle, but does not pass through the centre, is known as a chord.Part of the circumference is an arc.

diameter

chord

radiustangent

arc

Explanation

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April 13, 2023

diametercircumferenceObject circumferencediameter

Jamal gathered together five circular objects.He measured them, to find out how many times bigger the circumference of each object was, compared to the diameter.

Jamal was surprised to discover that no matter what size the object he measured, the circumference of the object was always about three times bigger than the diameter.

These are his results, in centimetres, to 1d.p.

This approximate relationship can be written ~~C 3 × d

Clock

Airfix potCan of LiltBiscuit tinTin of Beans

258.4

7.21.7

34

77.626.698.922.1

5.5

3.13.22.93.13.2

Explanation

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April 13, 2023

People have known for thousands of years that that the ratio of the circumference to the diameter of a circle is constant.Accurate measurements have shown the circumference to be approximately 3.142 × the diameter, but in actual fact the number is never ending and does not show any recurring pattern. As an irrational number, we use a Greek letter to denote it.

π or=C × d π=C d

If you know the radius, rather than the diameter, then

π or=C × 2r 2π=C r

This makes it an irrational number.

That letter is π, pi,or so,

Your calculator will have a button for the value of π. ππ

Explanation

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April 13, 2023

Circumference = Circumference =

As pi is such a long number, you need to write your answers to a small number of decimal places.

A circle has a diameter of 16cm. What is its circumference?

πd

16cm

π ×16=

50.2654825… =

50.3cm, to 1 d.p.

Example

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April 13, 2023

Circumference = Circumference =

As pi is such a long number, you need to write your answers to a small number of decimal places.

A circle has a radius of 7cm. What is its circumference?

2πr

7cm

π ×16=

43.9822972… =

44.0cm, to 1 d.p.

2 ×

Example

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April 13, 2023

20 = πd20 πd=

You can also work out the diameter, or radius of a circle, if you know the circumference.

A circle has a circumference of 18m. What is its diameter? 1

8m

C = πd

To find d, divide both sides by π

6.366197…

d =

The diameter of the circle is 6.37m, to 2 d.p.

Example

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